Obviously, any local improvement is impossible when both players already use a best response to each other (given their objectives). However, even in the standard case of two players with selfish objectives, very little is known about the corresponding set of all Nash equilibria among the memory-one strategies. Most available results address games without discounting, \(\lambda \!=\!1\) . For such games, Akin [1]} described all Nash equilibria profiles \(\left(\mathbf {p},\mathbf {q}\right)\)  that sustain full cooperation in the prisoner's dilemma. Stewart and Plotkin [2]} describe all symmetric Nash equilibria \(\left(\mathbf {p},\mathbf {p}\right)\)  among the memory-one strategies for all \(2\times 2\)  games. For generic cases (with \(R\!\ne \!P\)  and \(T\!\ne \!S\) ) they find that in addition to the equalizer strategies of the form Eq. REF , there are three more classes of equilibrium strategies \(\mathbf {p}\) :
